Particles unaffected by force fields
In order to make lanterns being affected you should increase the mass of your particles and decrease the Gravity in the Force Field settings. 

Clear the Effector Group

First thing to change is to clear the Effector Group in the Field Weights options (or create another group from the force fields). From the wiki: 


  The Field Weight Panel allows you to control how much influence each type of external force field, or effector, has on the particle system. 


Thus the effector is the one who affects on the particles, not the one who is being affected. And in your file, the group which contains meshes and lamp was set as effector.

Increase the mass of the particles

In the Physics scroll increase the mass of the particles. As they were too lighweight they began to fly away immediately.